HMN 2025: How Detecting strong-to-weak symmetry breaking might be impossible

When a system undergoes a transformation, yet an underlying physical property remains unchanged, this property is referred to as “symmetry.” Spontaneous symmetry breaking (SSB) occurs when a system breaks out of this symmetry when it is most stable or in its lowest-possible energy state.

Recently, physicists realized that a new type of SSB can occur in open quantum systems, systems driven by quantum mechanical effects that can exchange information, energy or particles with their surrounding environment. Specifically, they realized that the symmetry in these systems can be “strong” or “weak.”

A strong symmetry entails that both the open system and its surrounding environment individually obey the symmetry. In contrast, a weak symmetry takes place when the system and the environment only follow a symmetry when they are taken together.

When a strong symmetry is spontaneously broken down to a weak symmetry, new phases of matter can emerge. While this idea has been widely discussed, detecting this transition from strong to weak symmetry has proved highly challenging.

Researchers at the University of Texas at Austin carried out a study aimed at clarifying whether detecting mixed-state strong-to-weak SSB is in fact possible.

Their paper, published in Physical Review Letters, shows that no efficient protocol could reliably detect this transition, as even the most sophisticated techniques would be unable to distinguish between some symmetric states and symmetry-broken ones.

“Physicists are always looking for new phases of matter,” Matteo Ippoliti and Xiaozhou Feng, co-authors of the paper, told Phys.org.

“A very useful way of thinking about phases of matter is in terms of SSB. For example, the atoms in a solid break the symmetry of space by forming a crystal lattice, as opposed to atoms in a gas which may be found anywhere in space with equal probability.

“This symmetry breaking is spontaneous in the sense that it is not imposed from the outside, but rather, it is a consequence of the interactions between the atoms themselves and can be used as a definition for phases of matter.”

A long-standing physics challenge

Strong-to-weak spontaneous symmetry breaking (SW-SSB) has become the focus of numerous physics studies. Nonetheless, so far no one has been able to observe or detect this transition experimentally.

“A major puzzle has been how to tell whether a system exhibits SW-SSB,” said Ippoliti and Feng.

“For conventional SSB, that’s very easy: you can measure an ‘order parameter,’ like the magnetization of a magnet, which gives direct evidence of SSB. However, for SW-SSB the situation is very different: all order parameters proposed so far are information-theoretic quantities that are hard to measure, in the sense that they require a prohibitively large (up to exponential in the number of particles) amount of experimental data.”

The primary objective of this study was to determine whether SW-SSB is undetectable or whether more efficient tools or protocols could enable its detection. To do this, they built on recent literature rooted in the field of quantum cryptography, which focuses on the use of quantum mechanical effects to protect communications or hide information.

“The idea behind our approach is simple: we ‘encrypt’ certain states that lack SW-SSB in such a way that no efficient experiment can tell them apart from states that do have SW-SSB,” explain the authors.

“This shows that there can’t be a general, efficient protocol that detects SW-SSB: if such a protocol existed, it could be used to distinguish the two sets of states, leading to a contradiction.”

As part of their study, the researchers tried to construct an encryption that did not influence the presence or absence of SW-SSB in a mixed-state system. Ultimately, they were able to achieve this for two renowned and commonly observed symmetries, a discrete symmetry observed in certain magnets and a continuous symmetry that is relevant to superconductivity.

The team’s conclusions and implications for future research

Using techniques rooted in quantum cryptography, Feng, Ippoliti and Cheng showed that no existing protocols can distinguish between mixed quantum states that do and do not undergo SW-SSB. This suggests that detecting this transition is fundamentally difficult, irrespective of the tools used.

“Our work answers a key open question: can one detect SW-SSB efficiently?” said Feng and Ippoliti.

“We show that the answer, in the most general case, is no: the order parameters known today, which may require an exponential amount of data, are essentially the best one can do without further hints. This rules out the possibility of learning these phases from quantum experiments in a scalable way, including by AI and machine learning approaches.”

In the future, this study could potentially inspire other physicists to explore aspects of quantum many-body physics using concepts related to cryptography. Meanwhile, the researchers plan to improve the cryptography-based methods they employed and use them to conduct further research.

“Our work applies to a ‘black box’ situation that is very natural in cryptography but arguably less so for physics,” add the authors.

“In this idealized situation, the experimentalist is given access to copies of a quantum state without any further context. In reality, quantum experiments have access to a lot of prior information on the system which could be leveraged to improve learning protocols, including potentially detecting SW-SSB.

“In the future, it will be interesting to incorporate more of this prior information and sharpen the requirements for efficient learning of phases of matter in open systems. It will also be interesting to apply this approach to other types of phases or phenomena in quantum matter.”

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